On Warnaar's elliptic matrix inversion and Karlsson脙脙脙脙脙脙Minton-type elliptic hypergeometric series

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• 作者：Rosengren ; Hjalmar ; Schlosser ; Michael
• 关键词：11F50 ; 15A09 ; 33D15 ; 33E05 ; Matrix inversion ; Elliptic hypergeometric series ; Karlsson脙脙脙脙脙脙Minton-type hypergeometric series
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2005
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：June 1, 2005
• 卷：178
• 期：1-2
• 页码：377-391
• 文件大小：244 K

摘要

Using Krattenthaler's operator method, we give a new proof of Warnaar's recent elliptic extension of Krattenthaler's matrix inversion. Further, using a theta function identity closely related to Warnaar's inversion, we derive summation and transformation formulas for elliptic hypergeometric series of Karlsson–Minton type. A special case yields a particular summation that was used by Warnaar to derive quadratic, cubic and quartic transformations for elliptic hypergeometric series. Starting from another theta function identity, we derive yet different summation and transformation formulas for elliptic hypergeometric series of Karlsson–Minton type. These latter identities seem quite unusual and appear to be new already in the trigonometric (i.e., p=0) case.